1. Field of the Invention
The present invention relates to methods for statistically reconstructing images from a plurality of transmission measurements such as scans having energy diversity and image reconstructor apparatus utilizing the method. The invention can accommodate a wide variety of system configurations and measurement noise models including X-ray CT scanners and systems that use gamma sources with multiple energies, such as some SPECT transmission scans.
2. Background Art
Tomographic images of the spatial distribution of attenuation coefficients in the human body are valuable for medical diagnosis. Most hospitals have CT scanners for producing such images. Attenuation images are also useful in a variety of scientific studies, in industry for non-destructive evaluation, and for security purposes like baggage inspection. X-ray CT scanners are also being integrated into SPECT and PET scanners to provide accurate attenuation correction for emission image reconstruction and for precise anatomical localization of the functional features seen in the emission images.
Material attenuation coefficients depend on the energy of the incident photons. In clinical X-ray CT imaging, the source of the X-ray photons, bremsstrahlung radiation, has an inherently broad energy spectrum. Each photon energy is attenuated differently by the object (body). When such transmission measurements are processed by conventional image reconstruction methods, this energy-dependent effect causes beam-hardening artifacts and compromises quantitative accuracy. To avoid these difficulties, one could employ a radioisotope source with a monoenergetic spectrum, but the practical intensity is usually much lower leading to lower SNR. Recently developed fluorescence-based X-ray sources have somewhat improved intensity but still are lower than clinical CT sources. Higher intensities are obtained from monoenergetic synchrotron sources, which are expensive currently. Many gamma-emitting radioisotopes also emit photons at several photon energies.
U.S. Pat No. 6,507,633 discloses a statistical method for reconstructing images from a single measured X-ray CT sinogram. That method was the first statistical approach to include a complete polyenergetic source spectrum model in a penalized-likelihood framework with a monotonically converging iterative algorithm. DeMan et al. in xe2x80x9cAn Iterative Maximum-Likelihood Polychromatic Algorithm for CT,xe2x80x9d IEEE TR. MED. IM., 20(10):999-1008, October 2001 also proposed a solution to that problem based on a somewhat different object model and an algorithm that may not be monotonically converging. When only a single sinogram (for a given polyenergetic source spectrum) is available, usually one must make some fairly strong assumptions about the object""s attenuation properties to perform reconstruction. For example, one may segment the object into soft tissue and bone voxels or mixtures thereof.
The energy dependence of attenuation coefficients is an inconvenience in conventional X-ray CT. Alvarez and Macovski, as disclosed in U.S. Pat No. 4,029,963, showed how to approximate the energy dependence of attenuation coefficients in terms of a Compton scattering component and a photoelectric absorption component (or, roughly equivalently, electron density and atomic number) and how to separate these two components in the sinogram domain prior to tomographic reconstruction. The separate component images could then be combined to synthesize a displayed CT image at any energy of interest. Later enhancements included noise suppression, considerations in basis material choices, energy optimization, beam-hardening assessment and correction, algorithm acceleration, scatter correction, and evaluation of precision.
Numerous potential applications of dual-energy imaging have been explored, including rock characterization for petrochemical industrial applications, soil sample analysis in agriculture, bone mineral density measurements, bone marrow composition, adipose tissue volume determinations, liver iron concentration, explosives detection, detection of contrast agents in spinal canal, non-destructive evaluation, body composition, carotid artery plaques, and radioactive waste drums. Accurate correction of Compton scatter in X-ray CT may also benefit from dual-energy information.
More recently, there has been considerable interest in using X-ray CT images to correct for attenuation in SPECT and PET image reconstruction. In these contexts, one must scale the attenuation values in the X-ray CT images and from the X-ray photon energies to the energies of the gamma photons used in SPECT and PET imaging. Kinahan et al. in xe2x80x9cAttenuation Correction for a Combined 3D PET/CT Scanner,xe2x80x9d MED. PHYS., 25(10):2046-53, October 1998 have noted that accurate scaling from X-ray to PET energies may require dual-energy X-ray CT scans. This is particularly challenging in the xe2x80x9carms downxe2x80x9d mode of PET scanning. If the primary purpose of the dual-energy X-ray CT scan is PET attenuation correction (rather than diagnosis), then one would like to use low X-ray doses, resulting in the need for statistical image reconstruction methods to minimize image noise.
The conventional disadvantage of dual-energy methods is the increased scan time if two (or more) separate scans are acquired for each slice. This doubling in scan time can be avoided by methods such as alternating the source energy spectra between each projection angle or between each slice or conceivably in other arrangements. Special split detectors have also been proposed.
Prior to the 1990""s, all work on dual-energy X-ray CT used the FBP reconstruction method. In the early 1990""s, there were a few iterative methods published for dual-energy CT reconstruction. An iterative method to achieve beam-hardening correction and decomposition into basis materials is known. Markham and Fryar in xe2x80x9cElement Specific Imaging in Computerized Tomography Using a Tube Source of X-Rays and a Low Energy-Resolution Detector System,xe2x80x9d NUCL. INSTR. METH., A324(1):383-8, January 1993 applied the ART algorithm. Kotzki et al. in xe2x80x9cPrototype of Dual Energy X-Ray Tomodensimeter for Lumbar Spine Bone Mineral Density Measurements; Choice of the Reconstruction Algorithm and First Experimental Results,xe2x80x9d PHYS. MED. BIOL., 37(12):2253-65, December 1992 applied a conjugate gradient algorithm. These iterative approaches treat the problem as xe2x80x9cfinding the solution to a system of equations.xe2x80x9d These algebraic approaches can improve the accuracy relative to FBP methods, but they do not directly address the radiation dose issue. In contrast, in statistical image reconstruction approaches, the problem is posed as finding the images that best fit the measurements according to the (possibly nonlinear) physical model and a statistical model. Proper statistical modeling can lead to lower noise images, thereby enabling reductions in X-ray dose to the patient.
Statistical approaches have been extensively investigated, particularly in the last ten years, for monoenergetic transmission measurements. Recently, Clinthorne and Sukovic have investigated iterative algorithms for dual-energy and triple-energy CT reconstruction based on a weighted least-squares approach, including object-domain constraints in the following papers:
xe2x80x9cA Constrained Dual-Energy Reconstruction Method for Material-Selective Transmission Tomography,xe2x80x9d NUCl. INSTR. METH. PHYS. RES. A., 351(1):347-8, December 1994;
xe2x80x9cDesign of an Experimental System for Dual-Energy X-Ray CT,xe2x80x9d In PROC. IEEE NUC. SCI. SYMP. MED. IM. CONF., Vol. 2, pp. 1021-2, 1999; and
xe2x80x9cPenalized Weighted Least-Squares Image Reconstruction in Single and Dual-Energy X-Ray Computed Tomography,xe2x80x9d IEEE TR. MED. IM., 19(11):1075-81, November 2000.
That work assumed monoenergetic measurements. Gleason et al., in the paper xe2x80x9cReconstruction of Multi-Energy X-Ray Computer Tomography Images of Laboratory Mice,xe2x80x9d IEEE TR. NUC. SCI., 46(2):1081-6, August 1999 hint at the need for ML solutions to the multi-energy problem. Table 1 summarizes the various dual-energy reconstruction methods:
An object of the present invention is to provide a method for statistically reconstructing images from a plurality of transmission measurements having energy diversity and image reconstructor apparatus utilizing the method wherein, by using multiple measurements with xe2x80x9cenergy diversity,xe2x80x9d i.e., a set of two or more energy spectra, one can avoid segmentation, eliminating one potential source of errors.
In carrying out the above object and other objects of the present invention, a method for statistically reconstructing images from a plurality of transmission measurements having energy diversity is provided. The method includes providing a plurality of transmission measurements having energy diversity. The method also includes processing the measurements with an algorithm based on a statistical model which accounts for the energy diversity to obtain at least one final component image which has reduced noise.
The method may further include providing a cost function based on the statistical model. The cost function may be minimized during the step of processing.
The cost function may have a gradient which is calculated during the step of processing. The gradient may be calculated by backprojecting.
The method may further include analyzing the at least one final component image.
The method may further include calibrating spectra of the measurements to obtain calibration data. The step of processing may utilize the calibration data.
The method may further include displaying the at least one final component image.
The gradient may be calculated by approximately using a subset of the measurements, such as an ordered subset of projection views, to accelerate the algorithm.
The cost function may have a regularizing penalty term.
The measurements may be dual-energy X-ray CT scans or may be transmission scans with differing energy spectra, such as X-ray sources with different tube voltages or different filtrations, or gamma-ray sources with multiple energies.
The cost function may include a log-likelihood term.
The cost function may consist solely of a log-likelihood function, which is called maximum likelihood reconstruction, or the cost function may consist of both a log-likelihood function and a regularizing penalty function, which is called penalized-likelihood or maximum a posteriori image reconstruction.
The method may further include preprocessing the measurements prior to the step of processing to obtain preprocessed measurements. The preprocessed measurements may be processed in the step of processing to obtain the at least one component image.
The log likelihood term may be a function that depends on a model for an ensemble mean of the transmission measurements, and the model incorporates characteristics of an energy spectrum.
The log-likelihood term may be a function of the transmission measurements, prior to any pre-processing such as taking a logarithm of the measurements.
The gradient of the cost function may be calculated using a parametric approximation, such as polynomials, tables, or piecewise polynomials.
The regularizing penalty term may be based on quadratic functions of linear combinations of voxel values or nonquadratic (edge-preserving) functions of such combinations.
Parameter constraints such as non-negativity of voxel values may be enforced during or after minimization of the cost function.
The processing step may be based on the preprocessed measurements and may use a cost function based on a statistical model for variability of the preprocessed measurements.
Further in carrying out the above objects and other objects of the present invention, an image reconstructor apparatus for statistically reconstructing images from a plurality of transmission measurements having energy diversity is provided. The apparatus includes means for providing a plurality of transmission measurements having energy diversity. The apparatus further includes means for processing the measurements with an algorithm based on a statistical model which accounts for the energy diversity to obtain at least one final component image which has reduced noise.
The apparatus may further include means for providing a cost function based on the statistical model, and the cost function may be minimized by the means for processing.
The apparatus may further include means for calculating a gradient of the cost function.
The means for calculating may calculate the gradient by backprojecting.
The apparatus may further include means for analyzing the at least one final component image.
The apparatus may further include means for calibrating spectra of the measurements to obtain calibration data, and the means for processing may utilize the calibration data.
The apparatus may further include a display for displaying the at least one final component image.
The means for calculating may calculate the gradient approximately using a subset of the measurements, such as an ordered subset of projection views, to accelerate the algorithm.
The cost function may have a regularizing penalty term.
The measurements may be transmission scans with differing energy spectra, such as X-ray sources with different tube voltages or different filtrations, or gamma-ray sources with multiple energies.
The cost function may include a log-likelihood term, or the cost function may consist of both a log-likelihood function and a regularizing penalty function, which is called penalized-likelihood or maximum a posteriori image reconstruction.
The cost function may include a maximum likelihood or penalized likelihood algorithm.
The apparatus may further include means for preprocessing the measurements to obtain preprocessed measurements. The preprocessed measurements may be processed by the means for processing to obtain the at least one component image.
The log likelihood term may be a function that depends on a model for an ensemble mean of the transmission measurements, and the model incorporates characteristics of an energy spectrum.
The log-likelihood term may be a function of the transmission measurements, prior to any pre-processing such as taking a logarithm of the measurements.
The gradient of the cost function may be calculated using a parametric approximation, such as polynomials, tables, or piecewise polynomials.
The regularizing penalty term may be based on quadratic functions of linear combinations of voxel values or nonquadratic (edge-preserving) functions of such combinations.
Parameter constraints such as non-negativity of voxel values may be enforced during or after minimization of the cost function.
The means for processing may process the preprocessed measurements and may use a cost function based on a statistical model for variability of the preprocessed measurements.
The above objects and other objects, features, and advantages of the present invention are readily apparent from the following detailed description of the best mode for carrying out the invention when taken in connection with the accompanying drawings.